Value-Added Real Effective Exchange Rates: Testing for Countries with High and Low Vertical Specialization in Trade

I. Introduction

Over the last two decades, a growing body of theoretical and empirical literature has concerned itself with the changing landscape of the international trade market. As globalization and trade liberalization have progressed, several papers have drawn attention to and analyzed the phenomenon of vertical specialization, or the use of intermediate imports as inputs to export production.2

Yi (2003) argues that vertical specialization has been a major explanatory force behind the growth in world trade since 1960.3 Similarly, Hummels, Ishii, and Yi (2001) provide evidence for a trend of steady growth in the vertical specialization share of exports between 1970 and 1990, finding that by 1990, the vertical specialization share of total exports across the countries studied accounted for 21 percent of total exports and 30 percent of total export growth.4 More recently, Bems, Johnson, and Yi (2011) found that vertical specialization was an important factor in the decline in global trade between 2008 and 2009, accounting for 32 percent of the drop in total trade over the period.5

In light of this work, the role of vertical specialization as an increasingly-important driving force behind trade growth and contraction cannot be ignored. This is especially true when considering that changes in the nature of export production could have considerable ramifications on the underlying assumptions of conventional models of competitiveness.6 Bems and Johnson (2012) consider the consequences of the emergence of vertical specialization on the theoretical framework used to construct conventional real effective exchange rates (REERs). They argue that increasing shares of vertical specialization in trade make standard REERs constructed using the Armington framework less appropriate.7 They propose a new method of constructing REERs to reflect the growth of vertical specialization, which they name the value-added real effective exchange rate.8 The authors demonstrate that important differences exist between the value-added real effective exchange rate (VAREER) and conventional measures of the real effective exchange rate, and suggest that increases in vertical specialization may mean that the VAREER may function as a better explanatory variable for trade fluctuations than conventional rates for a given country.9 This paper will test for the existence of a statistically-significant difference between these two exchange rates in an effort to prove the theoretical prediction of Bems and Johnson (2012).

As a first step toward empirically testing the theoretical work of Bems and Johnson (2012), this paper explores the following question: does a real effective exchange rate constructed to reflect value-added prices explain the variation in a country's exports better than conventional real effective exchange rates, if that country has a high vertical specialization share of exports? To answer this question, I test two broad hypotheses drawn from the theoretical arguments made by Bems and Johnson (2012): (1) that for a given country with high vertical specialization in trade, REERs constructed using value-added prices will explain changes in exports better than conventionally-constructed REERs, and (2) that REERs constructed using value-added prices will explain fluctuations in exports better for countries with high vertical specialization than they do for countries with low vertical specialization in trade. The first hypothesis addresses the suitability of the VAREER as a replacement for conventionally-constructed rates, and the second hypothesis addresses whether increased vertical specialization explains this suitability. Using evidence from papers on vertical specialization by Hummels, Ishii, and Yi (2001) and Breda, Cappariello, and Zizza (2008), I test these hypotheses using Belgium as a representative country with high vertical specialization and Germany as a representative country with low vertical specialization.10

II. Literature Review

Vertical Specialization

Hummels, Ishii, and Yi (2001) define vertical specialization as the use of "imported intermediate goods...by a country to make goods or goods-in-process which are themselves exported to another country."11 They analyze vertical specialization between 1970 and 1990 for 14 countries and find that vertical specialization as a share of total exports steadily rose for all of the OECD countries over the period examined.12 They also observe that the vertical specialization share of exports tended to be much higher for the smallest countries in the sample and lower for the largest countries.13

Expanding on the analysis done by Hummels, Ishii, and Yi (2001), Breda, Cappariello, and Zizza (2008) measure and compare the import content of exports for several European countries in 1995 and 2000. They find that after controlling for energy imports, Belgium had the highest vertical specialization share of exports in 1995 and 2000 in the sample, at 39.8 percent and 44.1 percent respectively, while Germany had the second lowest vertical specialization share of exports in 1995 and the third lowest in 2000, at 20.3 percent and 26.2 percent.14

Real Effective Exchange Rates

Bems and Johnson (2012) modify the Armingtom framework for constructing REERs to reflect trade in value added rather than in goods wholly produced within the exporting country.15 They base this revised framework on the claim that increased vertical specialization in world trade has changed the nature of trade competition between countries. Rather than competing against each other's similar goods on the world market, they now compete against each other's potential to add value to the supply chain.16

To reflect their theoretical revision, they devise a new method for calculating a country's REER by modifying both the price and trade-weight components.17 They refer to it as the value-added real effective exchange rate and present it as an alternative to the conventional REERs used by the ECB and IMF, among others.18 The method they use to construct the VAREER introduces two changes to the conventional technique: first, they construct new bilateral trade weights that reflect value-added trade rather than total trade, and second, they replace consumer prices with GDP deflator to better reflect the value-added component of trade competitiveness.19

As a next step, Bems and Johnson (2012) construct annual VAREERs for 42 countries between 1970 and 2009 and compare these values with each country's conventional REER over the same period.20 They conclude that there are important differences between the two measures of competitiveness, primarily due to the use of GDP deflator in place of consumer prices, rather than their revised construction of the bilateral trade weights.21

One problem with the VAREER as calculated by Bems and Johnson (2012) is that the data only exist to construct annual value-added bilateral weights between 1970 and 2009, since the authors rely heavily on annual input-output tables. The limited number of observations resulting from this technique does not provide a sufficient number of observations for reliable econometric results.22 As a result, Bems and Johnson are not able to test their hypothesis using regression analysis.

However, given the authors' findings on the greater significance of the price-component of their real effective exchange rate, it is possible to construct a modified VAREER that uses the conventional trade weights as constructed by Bayoumi, Lee, and Jayanthi (2006) but adds in GDP deflator as a proxy for value-added prices.23 This approach keeps true to the theoretical assertions of Bems and Johnson (2012), while sufficiently modifying their measure to rigorously test it against conventional real effective exchange rates.

Bayoumi, Lee, and Jayanthi (2006) develop the methodology that is currently used by the IMF for calculating the real effective exchange rate.24 However, unlike Bayoumi, Lee, and Jayanthi (2006), who calculate trade weights based on a three year period (1999-2001) and apply those weights to their entire sample, I update the bilateral trade weights yearly to increase the accuracy of my results.25

III. Methodology

Country Selection

This paper's analysis of the VAREER is conducted as a comparison of data from two countries: Belgium and Germany. These two countries were identified as a satisfactory pair for two main reasons. First, they differ significantly in terms of the share of their exports that is explained by vertical specialization. Both Hummels, Ishii, and Yi (2001) and Breda, Cappariello, and Zizza (2008) identify Germany as a nation with relatively low vertical specialization in trade.26 By contrast, Belgium is a prime example of a nation with high vertical specialization in trade. Breda, Cappariello, and Zizza (2008) identify it as the nation with by-far the highest level of vertical specialization among the major European countries they examine.27

Second, the two countries are sufficiently homogenous, save for differences in economic size and vertical specialization, thus making it less likely that any observed differences in the regression will be driven by omitted variables. Geographic affects are minimized by the selection, as the two share a common border. Both countries possess federal governments, are members of the OECD, European Union, and the Eurozone, and share many of the same major trading partners. In terms of trade, the two countries are very closely tied to the EU. Between 1997 and 2012, 63 percent of German imports and 71 percent of Belgian imports came from the EU, while 64 percent of German exports and 76 percent of Belgian exports came from the EU.28

Hypotheses and Tests

I test two broader hypotheses that will help determine whether the VAREER is a suitable replacement for the conventional REER for countries with high vertical specialization. The first hypothesis is that the VAREER performs better than conventional REERs as an explanatory variable of export demand for countries with high vertical specialization in trade. I study Belgium and Germany in order to test this hypothesis. Breda, Cappariello, and Zizza (2008) provide evidence that vertical specialization constitutes a high level of Belgian exports, and a low level of German exports.29 This first conceptual hypothesis can be tested more directly using regression analysis by being broken down into the following four sub-hypotheses:

Hypothesis 1a: The Belgian VAREER will yield coefficients with a statistically-significant joint distribution as a regressor for Belgian exports.

Hypothesis 1b: The German VAREER will fail to yield coefficients with a statistically-significant joint distribution as a regressor for German exports.

Hypothesis 1c: The conventional Belgian REER will fail to yield coefficients with a statisticallysignificant joint distribution as a regressor of Belgian exports.

Hypothesis 1d: The conventional German REER will yield coefficients with a statistically-significant coefficient joint distribution as a regressor of German exports.

To confirm the theory of Bems and Johnson (2012) that high levels of vertical specialization in some countries make the VAREER more suitable than the REER, I should find that the VAREER is a more significant regressor than the REER for Belgium, the high vertical specialization country, and a less significant regressor than the REER for Germany, the low vertical specialization country. Hypothesis 1a and 1c test for whether the VAREER is superior to the REER in Belgium and 1b and 1d test for whether the REER is superior to the VAREER in Germany. Hypothesis 1c specifically tests the assertion by Bems and Johnson that the REER will be unsuitable for countries with high vertical specialization.

While the formulation of these sub-hypotheses may appear to create prohibitively strong statistical significance requirements to reach a definite conclusion, this is due to the nature of the testing and data. As of yet, there remains no systematic econometric means of comparing the relative significance of the joint distributions of different variables across different regressions of this type other than through direct comparison of the relative size of each of the F-statistics in question or through assessment of the statistical significance (or lack of statistical significance) of each individual joint distribution. Comparison through a simple panel regression presents a problem because the corresponding joint significance tests do not give information about which measure may be superior to another, only about whether there is a statisticallysignificant difference between the two. The inclusion of a euro interaction term attached to each REER only further complicates comparison via panel regression. Thus, I have constructed the sub-hypotheses to be accommodating to the latter method, since clear differences in statistical significance can justify strong conclusions about the relative explanatory power of different coefficients. However, should the individual joint significance results not meet the stringent conditions specified above, I will also engage in direct comparison of the magnitudes of the F-statistics of each of the REER measures to see if they properly correspond to the results that the theory would predict.

Since the variables included in trade estimation equations traditionally tend to be co-integrated, Hypotheses 1a-d will be tested using an error correction model (ECM) based on the work of Engle and Granger (1987) to estimate the long-run and short-run effects of the conventional REER and VAREER on exports. The use of an error correction model here draws on the procedure of a wide range of papers dealing with trade estimation through ECMs, including Chowdhury (1993). Employing this method also reflects the frequently observed comovements of trade time series, and is superior to a simple AR Distributed Lag (ARDL) regression since the ECM examines both long-run and short-run effects of the regressors on the dependent variable. In this case, the Engle-Granger test for co-integration is also preferable to the Johansen procedure because of the primary interest of this paper in the trade equation and the one-directional relationship between REERs and trade.

Since Bems and Johnson (2012) draw specific attention to the suitability of REERs for assessing export competitiveness, I analyze exports rather than imports.30 For initial reference, I define the export demand function for each country to be as follows, drawing from Khan (1974):31

Here, for country i and time t, X represents export demand, W represents OECD real GDP, REER represents the real effective exchange rate, and v the error term. As a method of testing the hypotheses above, I replace Khan's relative export prices with the REER. This should not be problematic for either the conventional or value-added REER, as both consumer prices and GDP deflator take export prices into account. From this simple export demand equation, I then conduct the two-step Engle-Granger test for co-integration and construct an ECM to estimate the long-run and short-run effects of the REER on exports.

As Engle and Granger (1987) explain, multiple non-stationary series that are first-order integrated may become integrated of order zero if a stationary equilibrium relative to each other is formed when a linear combination of them is taken.32 Such a relationship can then be reliably estimated using an ECM.33

Co-integration is dependent on the co-movements of the variables in question. The Engle-Granger method involves first estimating a long-run equilibrium equation of the variables of interest and then testing the residuals for stationarity using the Augmented Dickey-Fuller test.34 If the residuals are found to be stationary, then we can be confident that the variables are co-integrated, and can estimate an ECM to analyze the relative significance of the REERs being tested.35

My first step is to confirm the order of integration of the variables to be tested. To do so I run an Augmented DickeyFuller test on the levels and first differences of the dependent variable and the regressors to confirm that the levels are integrated of order one and the first differences are stationary. The test is based on the following model:36

Here, Δ denotes the first difference operator. Yit represents any time series variable. q is the optimal number of lags of the first differences, which I determine using Schwartz-Bayesian information criterion.37 The null hypothesis of the ADF is H0 : b1 = 0, which is tested against the alternative that Ha : b1 < 0.38 If the Dickey-Fuller test statistic testing b1 exceeds the critical value, then we can reject the null hypothesis that the series is non-stationary.39

Next, I use the Khan (1974) export demand function to construct four long-run equilibrium relationships, one regressed over the conventional REER and one regressed over the VAREER for both Belgium and Germany. Each relationship also includes an interaction with a dummy variable for the Eurozone period denoted by δeuro, which takes on δ = 0 before 1999Q1 and δ = 1 after, since a large break in the exchange rate data occurs when Belgium and Germany adopt the euro. For country i and time t, the long-run relationships are written as follows:40

If the variables in the long-run relationship are co-integrated, the residuals should be stationary.41 To test this, the second part of the Engle-Granger test regresses each residual over its lagged value:42

Here, v^t-1 represents the lagged residual. As with the Dickey-Fuller test for stationarity, the null hypothesis of nonstationarity, H>0 : b1 = 0, is rejected when the test statistic of b1 exceeds the critical value.43 Rejection of the null hypothesis implies co-integration of the variables in the long-run relationship.44

The Engle-Granger ECM allows for an examination of the long-run and short-run effects of the REER on exports by regressing the dependent variable over the lagged residual (representing the long-run relationship), and the lagged first differences of OECD real GDP and the appropriate REER.45 Thus the ECM takes the form below:46

I test for Granger-causality on the coefficients of the valueadded and conventional REERs in the short-run, and on the coefficient on the lagged residual of each regression, representing the long-run relationship. To be in line with the theory of Bems and Johnson (2012), I expect the Belgian VAREER and the German conventional REER to be "Granger causal," and the Belgian conventional REER and German VAREER to be "Granger non-causal."47

One shortcoming of the Engle-Granger ECM is that it fails to set optimal lags for the short-run lagged differences of the regressors. Thus, to get a more accurate picture of the shortrun I construct four autoregressive distributed lag (ARDL) models using the stationary first differences of the log variables. Using the setup outlined by Stock and Watson (2011), I construct the ARDL models as follows:48

Here n denotes the optimal number of lags for each variable, with θ, Φ, ω, and α representing the number of periods lagged in each instance. Using F-statistics on the coefficients of the value-added and conventional REERs, I test for Grangercausality on the predictive value of the total lags of the REERs and interaction terms.49

The key addition of the ARDL, the optimal number of lags, n, is selected using the Schwartz-Bayesian information criterion (SBIC). I regress the dependent variable several times over an increasing number of lags for each independent variable. The optimal number of lags is chosen from the regression that minimizes the following:50

θ is the number of lags in the regression, while T is the total number of observations in the sample. T remains fixed over the various regressions in order for the lag selection to be accurate. I have chosen the SBIC over the Aikake information criterion (AIC) because the SBIC is more accurate in large samples, as the AIC tends to overestimate n on average.51

In order to thoroughly test the second conceptual hypothesis, which states that REERs constructed using value-added prices will explain fluctuations in exports better for countries with high vertical specialization they do for countries with low vertical specialization in trade, I plan to directly compare the joint significance of the VAREERs for Germany and Belgium using an autoregressive panel regression of exports over lags of world income and lags of the VAREER. The two subhypotheses associated with this panel regression test the joint significance of the VAREERs as predicted from the theory in Bems and Johnson (2012). They are:

Hypothesis 2a: The VAREER will yield coefficients with a statistically significant joint distribution when regressed over Belgian exports.

Hypothesis 2b: The VAREER will fail to yield coefficients with a statistically significant joint distribution when regressed over German exports.

This method offers a more systematic approach to control for any confounding factors or differences between the two countries not uncovered in the regressions addressing the first conceptual hypothesis. For country i and time t, the panel regression is constructed using the following setup:52

As above, Δ denotes the first difference operator and n constitutes the optimal number of lags determined by SBIC. First differences are used to satisfy the same stationarity arguments that are relevant with the ARDL model. For the panel regression, I use the same lags as the individual ARDL regressions for ease of comparison. The crucial interaction term for the panel is δBEL, which is equal to 1 when the data regressed belongs to Belgium, and is 0 otherwise. δeuro, representing use of the euro as the national currency, is once again included as an interaction term with the VAREER of each country. Though Germany and Belgium share many important similarities, I also add a fixed effects term, zi, as a precaution against further time-invariant differences between the two countries.Continued on Next Page »